I still need to reread the paper in more detail, but an argument for common priors meaning identical or shared knowledge(both people have the same knowledge base not information transfer from one to the other). There was also a counter argument but it seem like a weak argument to me at my last reading.

From lesswrong wiki on priors:

This requires that, even in advance of seeing the evidence, you have beliefs about what the evidence means - how likely you are to see the evidence, if various hypotheses are true - and how likely those hypotheses were, in ad